Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases.

Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed to understand some blood diseases characterized by very long period oscillations in circulating blood cells. A system of three differential equations with delay, corresponding to the cell cycle duration, is proposed and analyzed. The existence of a Hopf bifurcation at a positive steady-state is obtained through the study of an exponential polynomial characteristic equation with delay-dependent coefficients. Numerical simulations show that long-period oscillations can be obtained in this model, corresponding to a destabilization of the feedback regulation between blood cells and growth factors, for reasonable cell cycle durations. These oscillations can be related to observations on some periodic hematological diseases (such as chronic myelogenous leukemia, for example).